{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "a752122c-4202-4ba0-aac5-cafec874dbcc",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.sparse import diags, csr_array\n",
    "from scipy.sparse.linalg import spsolve, gmres\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "db94c5d0-e347-4cf4-a955-c044e535d812",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. ])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# np.linspace(start, stop, N)\n",
    "x = np.linspace(0, 1, 11)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "9bd39398-d17b-424f-86ef-9a9a372799e3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# np.arange(start, stop, step)\n",
    "# 不包括stop这个值\n",
    "x = np.arange(0, 1, 0.1)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "8a0e1c38-ad98-46b0-ab9a-c9d911c518ef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
       "       [ 1., -2.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
       "       [ 0.,  1., -2.,  1.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  1., -2.,  1.,  0.,  0.,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.,  1., -2.,  1.,  0.,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.,  0.,  1., -2.,  1.,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.,  0.,  0.,  1., -2.,  1.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.,  0.,  0.,  0.,  1., -2.,  1.,  0.],\n",
       "       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  1., -2.,  1.],\n",
       "       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  1., -2.]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Dirichlet 边界\n",
    "# D_xx\n",
    "A = diags([1.0, -2.0, 1.0], [-1,0,1], shape=(10,10))\n",
    "A.toarray()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "9f904f15",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  1.],\n",
       "       [ 1., -2.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
       "       [ 0.,  1., -2.,  1.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  1., -2.,  1.,  0.,  0.,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.,  1., -2.,  1.,  0.,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.,  0.,  1., -2.,  1.,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.,  0.,  0.,  1., -2.,  1.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.,  0.,  0.,  0.,  1., -2.,  1.,  0.],\n",
       "       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  1., -2.,  1.],\n",
       "       [ 1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  1., -2.]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = diags([1.0,1.0, -2.0, 1.0,1.0], [-9,-1,0,1,9], shape=(10,10))\n",
    "A.toarray()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "bb63d5fc-44b4-41ee-9f2b-c2b849df78ae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
       "       [ 1., -2.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
       "       [ 0.,  1., -2.,  1.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  1., -2.,  1.,  0.,  0.,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.,  1., -2.,  1.,  0.,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.,  0.,  1., -2.,  1.,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.,  0.,  0.,  1., -2.,  1.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.,  0.,  0.,  0.,  1., -2.,  1.,  0.],\n",
       "       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  1., -2.,  1.],\n",
       "       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  1., -2.]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = diags([np.ones(9), -2.0*np.ones(10), np.ones(9)], [-1,0,1])\n",
    "A.toarray()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "9bee664c-eae3-40a7-bd19-bc8f4ef1d648",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<10x10 sparse matrix of type '<class 'numpy.float64'>'\n",
       "\twith 28 stored elements (3 diagonals) in DIAgonal format>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "544ea0f4-be5c-4efb-9e50-91edabca7e3c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.5, -3. , -4.4, -5.6, -6.5, -7. , -7. , -6.4, -5.1, -3. ])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = csr_array(A)\n",
    "# u = A^{-1}x\n",
    "# Au = x\n",
    "# 矩阵分解的算法\n",
    "# LU,QR\n",
    "spsolve(A, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "83b7e0c2-8063-4d5f-a011-98630caa0962",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.5, -3. , -4.4, -5.6, -6.5, -7. , -7. , -6.4, -5.1, -3. ])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Matrix free\n",
    "# |Au - x|\n",
    "gmres(A, x)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "558f33c2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.96154891, 0.25329603, 0.57485568, 0.18861549],\n",
       "       [0.68488405, 0.13137278, 0.60723589, 0.68626189],\n",
       "       [0.47137328, 0.47655576, 0.18750558, 0.35204462]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol = np.random.rand(3,4)\n",
    "sol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "684f4a90",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.96154891, 0.25329603, 0.57485568, 0.18861549, 0.68488405,\n",
       "       0.13137278, 0.60723589, 0.68626189, 0.47137328, 0.47655576,\n",
       "       0.18750558, 0.35204462])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = sol.reshape(-1)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "494ca536-57eb-43f4-9a86-66ac216b5fa0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f8abbfe5480>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0, 1, 101)\n",
    "# element wise\n",
    "u0 = np.where(np.logical_and(x > 0.4, x < 0.6), 4.0, 0.0)\n",
    "\n",
    "# 少写循环\n",
    "plt.plot(x, u0, label=\"u(x,t=0)\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "e3a7526b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False, False, False, False, False, False, False, False, False,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "       False, False, False, False, False,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True, False, False, False,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "       False, False])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.logical_and(x > 0.4, x < 0.6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c7663e10-51a9-442c-95fb-c8b6aa674d1f",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Diffusion(object):\n",
    "    # Initialization of constants \n",
    "    # u_t = cu_xx\n",
    "    def __init__(self, u0, c, x, dt, T):\n",
    "        self.u0 = u0\n",
    "        self.c = c \n",
    "        self.x = x   \n",
    "        self.Nx = x.size\n",
    "        self.dx = x[1]-x[0]\n",
    "        self.dt = dt  \n",
    "        self.T = T\n",
    "        self.t = np.arange(0, T+dt, dt)\n",
    "        self.Nt = self.t.size\n",
    "        self.sol = np.zeros((self.Nt, self.Nx))\n",
    "        self.sol[0,:] = self.u0\n",
    "        self.A = None\n",
    "        self.B = None\n",
    "    # Au = Bun\n",
    "    # theta格式\n",
    "    # u是下一个时刻的u\n",
    "    # un是当前时刻的\n",
    "    \n",
    "    # CFL number func.   \n",
    "    def CFL(self):\n",
    "        return np.abs(self.c*self.dt/self.dx**2)\n",
    "\n",
    "    # LHS Matrix assembly\n",
    "    def LHSMatrixAssembly(self, sigma, theta):\n",
    "        a1 = 2*theta*sigma+1\n",
    "        a2 = -theta*sigma\n",
    "        self.A = csr_array(diags([a2, a1, a2],[-1,0,1], shape=(self.Nx,self.Nx)))\n",
    "        return\n",
    "    \n",
    "    # RHS Matrix assembly\n",
    "    def RHSMatrixAssembly(self, sigma, theta):\n",
    "        b1 = -2*(1-theta)*sigma + 1\n",
    "        b2 = (1-theta)*sigma\n",
    "        self.B = csr_array(diags([b2,b1,b2],[-1,0,1], shape=(self.Nx,self.Nx)))\n",
    "        return\n",
    "    \n",
    "    # Solve\n",
    "    def Solve(self, method=\"explicit\", theta=None):\n",
    "        sigma = self.CFL()\n",
    "        print(\"cdt/dx^2 is:\", sigma)\n",
    "        un = np.copy(self.u0) # u in time tn\n",
    "        u = np.copy(self.u0) # u in time tn+1\n",
    "        if method == \"explicit\":\n",
    "            print(\"using explicit method\")\n",
    "            self.RHSMatrixAssembly(sigma, 0)\n",
    "            for ti in range(1, self.Nt):\n",
    "                u[:] = self.B @ un\n",
    "                self.sol[ti,:] = u\n",
    "                u, un = un, u\n",
    "        elif method == \"implicit\":\n",
    "            print(\"using implicit method\")\n",
    "            self.LHSMatrixAssembly(sigma, 1)\n",
    "            for ti in range(1, self.Nt):\n",
    "                u[:] = spsolve(self.A, un)\n",
    "                self.sol[ti,:] = u\n",
    "                u, un = un, u\n",
    "        elif method == \"theta\":\n",
    "            if (theta >=0) & (theta <= 1):\n",
    "                print(\"using theta method with theta=\", theta)\n",
    "                self.LHSMatrixAssembly(sigma, theta)\n",
    "                self.RHSMatrixAssembly(sigma, theta)\n",
    "                for ti in range(1, self.Nt):\n",
    "                    u[:] = spsolve(self.A, self.B @ un)\n",
    "                    self.sol[ti,:] = u\n",
    "                    u, un = un, u\n",
    "            else:\n",
    "                raise Exception(\"theta method should provide theta between \\[0,1\\]\")\n",
    "        return self.sol\n",
    "    \n",
    "    def plot(self):\n",
    "        ti = [round(self.Nt*p) for p in [0.0, 0.2, 0.4, 0.6, 0.8]]\n",
    "        ti.append(self.Nt-1)\n",
    "        for i in ti:\n",
    "            plt.plot(self.x, self.sol[i,:], label=\"t={:.3f}\".format(self.t[i]))\n",
    "        plt.legend()\n",
    "        return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "7bcd921f-8e52-46f6-ad6f-7266ed7bc2f1",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "c = 0.01\n",
    "x = np.linspace(0, 1,101)\n",
    "u0 = np.where(np.logical_and(x > 0.4, x < 0.6), 4.0, 0.0)\n",
    "dx = x[1] - x[0]\n",
    "sigma = 0.6\n",
    "dt = sigma*dx**2/c\n",
    "T = 1.0\n",
    "\n",
    "prob = Diffusion(u0, c, x, dt, T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "bc167420-3323-4de8-8eea-bd5cdfc028f8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cdt/dx^2 is: 0.6\n",
      "using theta method with theta= 0.6\n"
     ]
    },
    {
     "data": {
      "image/png": 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Vz01ISKBfv36Eh4cTERHBiRMnrth/7dq1tGnThsjIyDJVGq8HJeiKWs01Z7mkx5nTFdvec201W66WtveZKzEeXXpV3VSWS/VRVeVz77//fl555RUOHTrE9u3b8fHxqbR/ZmYmTz75JAsXLiQmJoa5c+de/+RKsGQLOjshxHYhxD4hRIwQ4v1y2gghxDdCiFghRLQQomo2YFTUO0pj6Febh753JiCg9d3WN6o8GvcG5wDzr4KrQHno1UdVlM89ePAgBoOBvn37AuDk5ISDg0Ol/WfOnMnw4cMJDjaXbr7wBWANLKnlUgjcLKXMEULYABuFEEullFsvajMQaFry6AT8X8m/CsV1cU1ZLiYj7J0FTfpcexGuq0WjhTZ3wcYvzZtOu5Qt5FQepR56PUtbTP7oIwoPWbd8rm14c/zefLPC81VRPvfo0aO4ubkxfPhw4uPjueWWW5g4cSIZGRkV9j969CjFxcX06tWL7OxsnnvuOe6///7rnL2ZKwp6yd6gOSVPbUoel7/7hgG/lbTdKoRwE0L4SymTrGKlot5yTVku8esgKxH6T6giqyqgzT3mRUz7Zpnz0y1Aeeg1g7XK5xoMBjZs2MCePXsIDg7mzjvvZOrUqQwdOrTC/gaDgV27drFq1Sry8/Pp0qULnTt3tkqhLouqLZZsEL0LaAJ8L6XcdlmTBsCpi54nlhy7RNCFEGOBsUDpzw2FojKuKcslZh7onSHMehsHWIRnYwjsADHzLRZ0IQRajah3WS6VedLVgbXK5wYGBtK2bVtCQ0MBuO2229i6dSsPP/xwhf0DAwPx8vLC0dERR0dHevTowb59+6wi6Bb9jpVSGqWUbYBAoKMQosVlTcr7tJV5h0opf5JSRkkpo7y9va/aWEX946rroRsNcPgf825CVbEy9EqED4XkaEiPt7iLVgjloVcD5ZXPLe8RERGBEKK0/C1QYfncDh06kJGRUerRr169+or9hw0bxoYNGzAYDOTl5bFt2zarFS27qiwXKWUmsBYYcNmpRODiLTsCgTPXY5hCAdeQ5XJyE+SlQUTZn7zVwoXrHlpkcRetRpTWfVdUHVVRPler1fLZZ5/Rp08fWrZsiZSSMWPGVNo/PDycAQMG0KpVKzp27Mijjz5KixaX+8jXxhVDLkIIb6BYSpkphLAHbgEmXdZsIfC0EGI25puh51X8XGENrnqT6EMLQWcPTW6pQqsqwb0R+LUy23HTsxZ10WmEquVSTcycOdPitqGhoWzfvr3M8aioKH755ZfS53379iU6Otri/gCvvPKKRV8qV4slHro/sEYIEQ3sAFZIKRcLIR4XQjxe0mYJEAfEAj8DT1rdUkW95KpCLiYTHFoMTW8BvWMVW1YJEUPN5XrPl82KKA+tVqg8dIVVsCTLJRpoW87xHy76WwJPWdc0heJiD90C3yNxu7nyYcRtVWvUlYi4DVZPgMOLodNjV2yu06gYusI6qD1FFbWaq/LQDy4011Rp2u+qryOlJDk3mYNpB4k7H4e/kz8RnhE0dG6IVqO9usG8moJ3uNkeCwS9Pma5KKoGJeiKWo3RWLJj0ZUEXUrzjcjGN19VZUWDycCcI3P4Zf8vpOanljnvoHPgzmZ3MrbVWJz0V7HNXMRQWP8p5JwDp8ozunQajfLQFVZBCbqiVlPqoV9p6f+ZPXA+AXq9bvHY25K2MXH7RGIzY+nk14nHWz1OuGc4oa6hnMk9w6G0Q2w+s5n/xfyPRXGLeK7dcwxtPBSNsCD8Ez4U1k0yh12iKq/Frjx0hbVQgq6o1Vic5XJkCQgNNLNsMdEv+3/h691f08CpAV/1/oqbg26+ZCVgmD6MMPcwhjUZxn0R9/Hx9o95Z9M7bD6zmQ+7fYiN5gp7k/pGmis9Hv7nioKuYugKa6GqLSpqNRbH0I8th6BO5lK2lSCl5Jvd3/D17q8ZFDKIBbctoE9wn3KXdV+ghVcLpg+cznPtnmNp/FJeWvsShcbCyu0Rwry46cQGKM6vtKnZQ1dZLlVNVZXPffXVV4mMjCQ8PJxnn30WWbKm4Er9d+zYgVarLV18ZA2UoCtqNRZluWSfhaR90LRvpWNJKflkxyf8vP9nRjQdwUfdPsJWa2uRHRqh4dGWj/JGxzdYc2oNz6x6hrzivMo7Ne0LhgI4sbHSZlqVh14tVEX53M2bN7Np0yaio6M5cOAAO3bsYN26dVfsbzQaee211+jfv//1T+wilKArajUXPPRKHfTYleZ/r5DdMuXAFH4/9Dv3ht/Lu13evfrsFeDu8LsZ33U825K38famt0u9sXJp2M28yOnYikrH1GlVDL06qIryuUIICgoKKCoqorCwkOLiYnx9fa/Y/9tvv2XEiBFWLZ0LKoauqOUYTSZ0GlFpSIRjy8HZH3wrXj69I3kH3+75loGNBvJqh1crH+8K3N70djILM/li1xfMODSDeyMq2OLOxg5Ce8Kxf0FOqnCjDW09zHLZ8MdRUk/lXLnhVeAV5ET3OyoucFUV5XO7dOlC79698ff3R0rJ008/TXh4OKmpqRX2P336NPPmzWP16tXs2LHjOmd9KUrQFbUag0lWHj83FsPxNRA5rELBPJd3jlfWvUJDl4a81/W96xLzCzwY+SB7Uvbw+c7PaeHVgjY+bcpv2LQvHF0GacfBq0m5TXQqy6XasVb53NjYWA4dOkRiYiJgLgOwfv36cottXej//PPPM2nSJLTaq/+FeCWUoCtqNUajrDzD5dR2KDxfYbjFYDLw8rqXyTPkMaX/FBxsHKxilxCCCd0mcOeiO3l53cv8MeQPPOzKuSHbpCSuf2x5hYKu1QgM9eymaGWedHVgrfK58+bNo3Pnzjg5mdcoDBw4kK1bt9K9e/cK++/cuZPRo0cDkJqaypIlS9DpdNx2223XPS8VQ1fUaq7ooR9bDhodhJS/0e7UmKnsTtnNuC7jaOzW2Kq2uehd+KLXF2QUZDBhawWbabg3BK9mZjsrQHno1UNVlM8NDg5m3bp1GAwGiouLWbduHeHh4ZX2j4+P58SJE5w4cYKRI0cyefJkq4g5KEFX1HKMJolOW8nb9NgKCO5S7urQxOxEftz3I32C+zA4dHCV2BfuGc7YVmNZcXIFG09XkM3StK+5rG9h+TFjrcpDrxaqonzuyJEjady4MS1btqR169a0bt2aIUOGVNq/KlEhF0WtxmCSaCqKeZ9PhJQY6PtBmVNSSiZun4gQgtc7Wr569Fp4qMVDLI5bzIdbP2TesHnY6S7bWKNpP9jyHcSvh+aDyvRXK0WrD2uXz9Vqtfz4449X1f9ipk6darE9lqA8dEWtxmSqJIZeSbri6lOrWZe4jqfaPIWfo18VWgh6rZ63O79NYk4iv+z/pWyD4C6gd6ow7KJCLgproQRdUaupNIZ+fA24NADvZpcczivOY+L2iTR1b8rd4XdXg5XQyb8Tt4beyq8HfiX+/GXbz+n0ENID4taW21d56AprcUVBF0IECSHWCCEOCSFihBDPldOmlxDivBBib8ljXNWYq6hvGE0mdOUV5jIZIX4dhPYqk644NWYqybnJvNP5nSvXXLEiL0e9jJ3Wjs93fl72ZGgvyIiHjBNlTqlqiwprYYmHbgBeklKGA52Bp4QQEeW02yClbFPyGG9VKxX1lgo99ORoyM8wC+VFZBRkMC1mGn0b9qWtT5l9WaoUL3svHm75MOsS17E3Ze+lJy/YWY6Xrjx0hbW4oqBLKZOklLtL/s4GDgENqtowhQJKslzKE/QLwnhZuuKU/VMoMBbwdJunq964cri7+d142HnwzZ5vLi0L4BVmXs1ajqDr6mEeuqJquKoYuhCiEebt6LaVc7qLEGKfEGKpECKygv5jhRA7hRA7y1uJpVBcjtlDL+dtGrcWfCLA2bf0UHJuMrMOz2JI6BBC3UKrz8iLcLBxYGyrsexI3sHWpK3/nRDC7KXHrTPvfXoRWo3AqIpzKayAxYIuhHAC/gKel1JmXXZ6N9BQStka+BaYX94YUsqfpJRRUsoob+/Kd3FRKKACD704H05ugdDelxz+KfonTJh4os0T1WhhWUaFjcLf0Z9vdl/mpYf2hvx0OLv/kvY6rcpDrw6uttrid999R5MmTRBCkJpadjerC0ybNo2mTZvStGlTpk2bVnq8ovK5M2bMoFWrVrRq1YquXbuyb9++a5/UZVgk6EIIG8xiPkNK+ffl56WUWVLKnJK/lwA2Qggvq1mpqLeUG0M/tQ2MhZfEzxOyEph3bB6jwkbRwMnyiKCUkvyYGFK++JLEZ58jfvgIjnbrTtyQoZx6/AmSP/qInE2bkEajxWPqtXqeaP0EB9IOsDph9X8nQkvCQ5eFXVQMvXq4WkG/6aabWLlyJQ0bNqywTXp6Ou+//z7btm1j+/btvP/++2RkZAAVl88NCQlh3bp1REdH88477zB27Njrm9hFWJLlIoApwCEp5RcVtPEraYcQomPJuGlWs1JRb7lQbfES4taal/s37Fp6aMqBKWg1Wsa0HGPRuKaCAtJ/m078bbdzYsRI0v73PwqPHUPr6YlTr57YBAdTnJRE5tw/OfXIo8Te0peUr7/GkGbZ23pI4yE0dGnIj9E//uelO/uZN4++TNBVlkv1cDXlcwHatm1Lo0aNKm3z77//0rdvXzw8PHB3d6dv374sW7as0vK5Xbt2xd3dHYDOnTuXFvayBpasFL0JuA/YL4TYW3LsTSAYQEr5AzASeEIIYQDygdGy0kLRCoVlGIzleOhxayGwI9iaCyKl5KWw6PgihjcdjrfDlUN5uZs3k/T++xSfTMCuZUv83h2Hy6BBaF1dy7Q1FRaSs3o1mX/PI+2HH8mYOQvfV17GdcSISqs26jQ6Hop8iPe2vMeWpC10DSj58gntBbumQnGBubwu9dNDXzP1J1JOxll1TJ+GofR+sGJv92rK50ZElJfIV5bTp08TFBRU+vxCmdy0tDSLyu9OmTKFgQMt2zbREq4o6FLKjUCl9UallN8B31nLKIXiAkaTxNbmoh+SeelwZi/0eqP00O8Hf8cojTwQ+UDlY2Vnk/zBB2QtXIS+YUOC//crjl26VNpHY2uLy8CBuAwcSOHx4yS9+y5Jb7/D+fkL8P/4I/QXfZgvZ0jjIXy/93t+PfDrpYK+7f/MYaOSEIzKcql+rlQ+11LK81uFEBUev5g1a9YwZcoUNm6sfEerq0HVclHUagwmicPFWS7x6wFZGj/PKsrij6N/0K9hP4KcKxbX4tOnSXjsMYpOnMTzicfxevxxNLaWbT93AdvGjWn422+c//tvzn7yKSfuuJPA77/HoV35+e56rZ57I+7ly11fEpMWQ6RnJDS6CYTW/CujRNDro4demSddHVypfK6lHnpgYCBr164tfZ6YmEivXr3w8vKqtPxudHQ0jz76KEuXLsXT0/O65nIxaum/olZTJsslfp25LkqDdgD8ceQPcotzebjFwxWOkb9/P/F3jsZwNoXgX37G57nnrlrMLyA0GtxGjiTkjzloXVxIePBBspYsqbD9qLBRONk48ev+X80HbJ0hMMo8jxJ0qtpitXA15XMtpX///ixfvpyMjAwyMjJYvnw5/fv3r7R8bkJCAsOHD2f69OmEhVm3LrwSdEWtpkyWS/wGc7ErrQ2FxkJ+P/g7Xfy7EO5ZdocYgNwtWzh53/1obG1pNHsWjp07W8UufaNGNJw9C7uWLTn94kukT/+93HbOemfuaHYHKxNWkpCVYD7YqLs5bFRgzv7VajRIaS5Epqg6rrZ87jfffENgYCCJiYm0atWqtGTuxeVzPTw8eOedd+jQoQMdOnRg3LhxeHiYNzqpqHzu+PHjSUtL48knn6RNmzZERUVZb5JSyhp5tG/fXioUV6LvF2vl49N3mp9kJUn5rouUG7+SUkr555E/ZYupLeSWM1vK7Zu3d6881LadPD5kqCxOTa0S+4yFhTLhqafkwWbNZca8eeW2SclNkW1/ays/2PKB+cDxNeZ5HPlXSinld6uPyYavLZaFxcYqsbG2cPDgwZo24YajvNcM2Ckr0FXloStqNZd46CdKbh416o6UkhmHZ9DMvRmd/DqV6Vd47BgJYx9D5+lJ0C8/o7NinPJiNHo9Db74AocunUl6622yV68u08bbwZtbQ29l4fGFZBVlQVAn0OrhxHqA0vnVtzi6wvooQVfUaowXC3r8erB1Bf/W7Dy7k2MZx7g7/O4y2QPFp0+T8MijaPR6gn+dgo2PT5XaqNHrCfz2O+wiIjj9/AvklrOpwd3N7ybfkM/8Y/PBxh4CO5jDR4C2xH6V6aK4XpSgK2o1lwj6iQ3mxUQaLbMOz8LV1pVBIZfuAGQqLCTxmWcx5eUR9MsvlaYVWhOtkyNBP/2ITYMGnH7+BYqTki45H+4ZTluftsw+MhuTNJnj6MnRkJ9ZOr/6oOdSLU+xmGt5rZSgK2o1pVku509Dehw06kZybjKrE1YzvOnwMtu9JX/wAQUHDxLwySTsmlXvzvI6d3cCv/8OWVBA4vPPYyqp3XGBu5vfzansU+a9Rxt1A2mChC2l9d7ruoduZ2dHWlqaEnULkFKSlpaGnZ3dlRtfhMpDV9RqSqstXoifh3RnzpE5SCSjm42+pG3G3Lmc//MvPB9/DOebb64Ba8E2NBT/jz/m9HPPcfbjj/F/993Sc30a9sHH3oeZh2bSo9dXoLWF+A1o3c1pcnU9hn4hY0RVWrUMOzs7AgMDr6qPEnRFrabUQz+xHuzcKPQK4691z9ArsBcBTv8t1MiPieHs+A9wvOkmvJ95xuLxs9LyOXUwnTOxmeRmFJKXVURBbjF6Ox0OrnocXGzxDXEhOMIDjwDHSpf7X8Clfz8KHn2EtF+mYN+6NW633QaAjcaGUc1G8f3e74nPSyIkqCOcWI/O83GAOp+LbmNjQ0hISE2bUadRgq6o1RiMJnOMOW4DNOrGspPLySjMuGSvUFNBAWdefQ2thwcBn32K0GorHbOowMDBjWeI2XCGzLN5ADi46HH1scfD3xFbJxuK8w3kZRVxLiGL47tT2PwXOLjqad7Zj5a9gnByr3xhkvfzz5O/dx9nP5iAQ1QH9IHmCpAjw0byU/RPzD48mzdCesCaj7AzmPPR67qHrqh6lKArajVGk8SzOBkyT0LnJ/njyB+EuIbQ0a9jaZtzX35F0fHjBE35BV1JFbvyKMgtZveyk8RsOE1RgRH/Jq606NGUoHAP3P0dKvS+s9MLOHUonRPRqexZnsDelado2sGXqEGNcPNxKLeP0OnwnziR+GHDSHrjDYKnTUVoNHjZe9GvUT8WHV/E850/wh6JX/ouwKvOe+iKqkcJuqJWYzBJQnL3AHDEM5joI9G82uHVUvHN3bqN9GnTcL/nHpxuuqncMaSUHN2WzKa/YinIKaZxOx/a3BKMb4iLRTY4e9gRcVMAETcFcP5cPtGrT3Fw0xlid6YQNaghbfs2RGtTNr9AH9gA3zffJOmtt0j/7Tc8H3wQMJcD+CfuH/4tTuU2Gwe803cAAzHW8ZuiiqpHCbqiVmM0SRpm7wZ7D+am7kav0TO08VDzuZwczrz5BvpGjfB5+aVy+2enF7Bq2iFOH8nAN8SFoc+1wSvQ+ZrtcfW2p/udYbTr35ANfxxj28J4jm4/y833h+MXWrb8ruvw28letYpzX3yJU7du2DZpQjufdoS6hjL3+DxuC+qE17ltwEDloSuuG5W2qKi1SCkxmCTBWXvIa9iZf+L/oV+jfrjamoUz5dPPMCSfJWDSRDT29mX6nzqYzh8f7iDlZBY9727GiFfaX5eYX4yjmy0DxrZg8NOtMRSZmPf5bg6sSyyTkieEwH/8+2gcHTnz5ltIoxEhBCPDRhJ9LpojARG4ZB3FjWwMal9RxXWiBF1RazFJaMA5XAvP8K+7DznFOYwMM+8Ak7dnD5lz5uBx//3Yt259ST9pkuxadoJF3+7FwVXPHW90oEWPBojLN8qwAg1beHLHWx0ICvdg3ayjrJ52CEPRpdvV6by88H3zDQqio8mYMweAIaFD0Gv0/EkOAJ00h9VNUcV1Y8kWdEFCiDVCiENCiBghxHPltBFCiG+EELFCiGghRLuqMVdRnzCYTHTSHAJgbv5JQl1DaefTDllcTPK776Hz98f7macv6WMymlj92yG2zo+jSXsfRr4WhZtv+TcurYWdow23PtmKDoNDOLwtmQVf7aEgt/iSNi6DB+PYtQvnvviS4pQU3Ozc6NuoL4tTtpOjs6OT5pAKuSiuG0s8dAPwkpQyHOgMPCWEuLxg8ECgacljLPB/VrVSUS8xmiSdNYfYZ+/O/vPHGRU2CiEE6dOmUXj0KH5vv4XG0bG0vaHYyLKfDnB4azIdh4TQ95FIbGwrT2G0FkIj6Dg4hAFjW5CSkM38L/aQe77wv/NC4DduHLKoiLMffwyYb47mFOeywLcZnTWHlIeuuG6uKOhSyiQp5e6Sv7OBQ8Dl26oPA34rqe64FXATQvhb3VpFvcJgknTSHGKmRyB6jZ4hjYdQlHiac999j1OfPjj36VPatqjAwOLvoonfl0r3O5vS4dYQixYBgTlWn52Wytn445zcv5dj2zZzYu8ukmOPknk2GZPJeOVBSmjc1ofBT7XmfGo+f3+2m6zU/NJz+kaN8HxsLNlLl5Gzfn3pzdH59oLmIgHy0y1/cRSKcriqLBchRCOgLbDtslMNgFMXPU8sOXZJhSIhxFjMHjzBwcFXaaqivmHKSMRXe441emduadgXV1tXEie9DRoNfm+/VdrOUGxkyf9Fc+bYeW55MJxmnSv3JaSUpJyII3bHVpJjj5AcF0tBdlaF7W1s7fAJaYxfkzBC20YRGNECjaZizz8o3INhz7Vh8Xf7WPDVHoa/3B5HN/NCJM8xY8ha/A/JEz4kdLF5Y+vPdn5GvF6LY/J2iGhyla+SQvEfFgu6EMIJ+At4Xkp5+bu/PFeozO9HKeVPwE8AUVFR6velolI0CZtY6WBPPsUMbzqc3C1byF6xEu8XXsDG3yzaRqOJf3+O4fTRTG55MIJmnfwqHC8nPY3oVcs4vGk9GUmnEUKDV1AwTaI64xvSGEcPD+wdndE7OFBcUEBBbg55WZmcOxFP8vGj7P13MbsWz8PB1Y1mXbrT6pYBeAU1LPdafqGuDHm2DQu+3MOCr/cy/KV22DnZoNHr8X3zTU6NGUPG9OkMvvs2vtz1JX84uXDv2W3A3eWOp1BYgkWCLoSwwSzmM6SUf5fTJBG4uE5pIHDm+s1T1Gd0pzYx19kVNxtforzacnLsSGwCA/F48AHAnM2y+rdDnIhOpcfosArFPDM5iR0L/yJm3UqMRiPBkS2JGnI7TTt2xd7ZssVFAMWFBcTv2cmRzRvYv+pf9ixbROOoTnQcNoqAsOZl2vs2cuHWJ1ux6Nt9LPp2L8Oeb4veXodT92449epF6uT/o/HQobTz6sZCwzoeO7v12l4ohaKEKwq6MAcipwCHpJRfVNBsIfC0EGI20Ak4L6VMqqCtQmERKac3sdvNhl5u/Tg/908Kjx2jwbfflG7wvPnvWI5uO0unYaG07FW2Kl1BTg6b/pjOvuVL0ei0tOjdl6ghI3DzrdiLrwwbWzvCOncjrHM38nOy2bN0EXuWLWLWzpcJbd+R3g+MLTN2g2bu9B/bgqU/7Gfpj/sZ/ExrtFoNPq+9StzQYaR89RU33zGYHefWsasogb75GWBfcfkChaIyLMlyuQm4D7hZCLG35DFICPG4EOLxkjZLgDggFvgZeLJqzFXUG86fZpHMBAkd9F1I/fobHDp3xvmWWwA4uOkMe1eeomWvQNoPuDTsIU0mDqxZwa8vPMa+5Utp3W8gj347hVsefeqaxfxy7J2c6TrqbsZ8/yvd736QUzH7mfrSE2yeO4PiosJL2oa08qL3vc1IPJzBxjnHkFJiGxKCx333cf7vebTLcEVX7MA8Z0c4ucUq9inqJ1f00KWUGyk/Rn5xGwk8ZS2jFArjiQ0scHbELjeIJv8sw5idje8bbyCE4PSRDNbNOEJwhAfdRjW5JJslJyOdZZO/5GT0HgKaRdDnrcfxaRRaZXbq7ezpOGwk4d17sW76r2z5cxZHt27i1mdfwbvhf6Viw7sGkJGUx54VCbj7O9CqdxBeTzzO+QULME3+hsKO7dnktZ6zcSvxbT6okisqFBWjVooqaiVbYhdxVqfD7lRr3JYvxG3ECOyahZGZksfSn/bj6mNPvzEt0Gj/ewsf37Wd3155mtOHD9LnkScZ/d7EKhXzi3H28GLwc68y4o33KcjJZsabL7B7yYJLSgF0vr0xjVp5sfGPY5yMSUPr7Iz3M88go/fS+qAHJiFYcGZDtdirqJsoQVfUSual78dVarlnRxxSp8PrmacpLjSy9If9ANz6VCts7c0/ME0mI+tn/I/5n4zHycOTez/+kjb9BiE01f/2btSmPfd/+h0NW7VlzbSfWfDZhxTlm2uuazSCvg9H4BHgxIopMWSl5uM2cgQiuCEPRa+nhfRgHjnIvIxqt1tRN1CCrqh1nE89zBobEyMzAul5OpqcYXei8/Zm7czDpCfl0u+RSFy9zcv5C/PyWPDpBHYs/ItWfQZw94TP8Qys2TUODi6u3PbqOHrdP4a4XduZNe5VzqecBUBvp2Pg4y2REpb9dACjFDg8/RxBOecYeiiQRBsdu2Jm1qj9ihsXJeiKWsc/+6ZQDPRcayDD1on820cTs+EMR7edpePgEIIjPAE4n3KWWe+8TPzeXfR5+An6jn0anV5fs8aXIISg/a3DGP7m+2SnnWPGmy+QeDgGMJfgveXBcM4lZLNhzjFse/XigGcIEWvj8CgwMj/+nxq2XnGjogRdUeuYn7SRYUeM2B05yYzm/SjIFmz44yjBkZ5EDWwEQGrCCWaNe4WcjDRGvDmeNv1vrVmjK6BRq7bcPeEL7Jyc+WvCOxzfZV5kHdLam3YDGnJw4xlO7UplSuRg9OczeWqHLcvzTpFXnFfDlituRJSgK2oVR9KPcLg4m+EbbTAGBLI6uBOn/jmFg4uevg9FIDSCM0cPM+e91wEY/d4kGrZsU7NGXwGPgAaMHv8JnkENWfDZhxxcvxqATkNCaNDMjZ3zjpPi2oi09jfRYkcxunzJv8fm1bDVihsRJeiKWsX8mN/pGWPC/lwx+fc+ys0FdhRlFdHv4UjsnGw4uX8vcye8hZ2zM3eN/wSv4EY1bbJFOLi4cse4DwmKaMHS779g99JFaLQa+j4Uic5Gw+A8PXGD70EUm3hgo4H5h+fUtMmKGxAl6IpaQ7GxmGXx/3LvehO2TRpxxr0NEcU6Arv54d/EjYQD+5g/aTxuvv6Mfv8TXH2ss0ioutDbO3D7a+/ROKoza6b+yJ5/F+PoZkuPe5rha9SQneSE69ChdNsLJ0/HkZCVUNMmK24wlKArag3rEtfRbmcuLlkCu8de5czqJE5pjQR38+dUTDTzJo3Hzc+fUe98iKPbjbk8XqfXM+SF12gc1ZnVv/7AvhVLCG3tzW69AY5mkz/wYTQIRm0wMT92fk2bq7jBUIKuqDUsjvmLUZtM6IOd2XzQGTTwj2MxOQnH+HvS+7j6+DLqnQ9xcCm7GfONhFZnw5AXXiO0XQdW/jKZg2uXs9a+GJOLDesWn8WhR1t67TexdeufGK+iFrtCoQRdUStIzU/FZeEGXHMhpdcYzsZn4dXTD9vic+z+5VOcPb3NYu7qVtOmWgWtzoYhL75JSJv2rPj5e0Lz4yiKcqcw30BMo4eQWrhleSrbki7fekChqBgl6IpawZLoPxmy1UhOqA97ExvTJMoHrWchQ88uRmdnz8i3xt+wYZaK0NnYMOTFNwgIC6dvygoM2fF0GhJKfLyW3NZt6HJYsn7NtJo2U3EDoQRdUeNIKTn/23Tsi3QcbfQIds56ogb5cGrml2ikiZuefgsXL5+aNrNKsLG14/ZXx3Hexg3t6v/hF1qAfxNXol0fINvZjaA5mzhfeL6mzVTcIChBV9Q4+49vpuuGdA63GUKmKZAeo0NY8s2HGHOzWOR7K+4BZWud1yXsnJxYETQMaevI/E/G0+FWT0waHcda303bY0bW/ftLTZuouEFQgq6ocY5P/pxCuxDOutxMeNMMopf/wrkT8XgOHcNZO1+0Gss2e76RKbJzJq/3w0ijkRU/TaRDd0mmLpL4ht3R/KJy0hWWoQRdUaPkJCcSvDKW/a0fwFGcw6A9TNzuHfR55HH0jSIB0NVA1cTqRqcRFDl5Mezlt8lKSebYoVU00O/jZMjtBCTYcHSVWjmquDJX/KQIIX4VQqQIIQ5UcL6XEOL8RbsZjbO+mYq6yoEvx5MYdCsGrTeBNjPZv2ULUUOG07rvIAwmcy3x+uChazUCo0kSGNGC/k88T+KhGIRmIxphYn/EPaR8/fUltdUVivKwxPWZCgy4QpsNUso2JY/x12+Woj5QnJyMcV0iiYF9aGCzkOizkqadutLj7gcBMBpNgNl7revoNJrSL7Dwbr246Y57iU0qJMD0MzkuzSnIbkrWxvU1bKWitnNFQZdSrgfSq8EWRT0j/psvOdr0HqQuiVOph/H2dWPgky+WbkxR6qFr676gX/DQL9Bp+J00b9eKY5nF2Njv5ViT2zn8xXfKS1dUirWCk12EEPuEEEuFEJEVNRJCjBVC7BRC7Dx37pyVLq24ESlKPM2RvZJcezdE/iJ0wsSw517Cxs6utM0FgasfHroo/QIDcz31fs+9g59DPvln11Ak04nX9SB7zZoatFJR27GGoO8GGkopWwPfAvMraiil/ElKGSWljPL29rbCpRU3Kse+mcbJwD7kF8+lOD+PYeFpuDRue0mb+hdDN11yzMbOnmE9/bDTFmMoXkiqeyi7f1qGvKydQnGB6xZ0KWWWlDKn5O8lgI0Qwuu6LVPUWQriT7DzdAMM+WvQ5KXSNzCBgFZdyrT7z0Ov+1kuWo3AYCwbTnGK6M2wgP1oDIUU5M7lsENXUhatrAELFTcC1/1JEUL4CSFEyd8dS8ZMu95xFXWXLV8t5bw+G2PRAVp370ik40kI6Vmm3QUPvR446Oi0l8bQSwnpiZ99Dv36tUUYUiko3snGv+KQRlW0S1EWS9IWZwFbgGZCiEQhxCNCiMeFEI+XNBkJHBBC7AO+AUZLdedGUQEp2w9xMMeJ4rzlmAJd6N3K2XwipHuZtkaTCZ1GUOIv1Gm0F2W5XIJXU3DyI9IxAdcukRiL9nJaayDmf8ur30hFrUd3pQZSyruucP474DurWaSos0iTZMWUnRTm/kO+vpihz7yIdsOH4N0cnMtuVmEwyXoRPwfzTdFyPXQhILQnxK7izqd28eGRO/FOX8GmTfY0ubMAO2e7sn0U9Za6H5xU1Br2/LGDlJwtSJlL3C2OtGoQCSc3Q+Oby21vNMp6keECJTH0im52Nr4Z8lJxzjqJ/YgoDFojuQWrWPXZ0uo1UlHrUYKuqBZyMgrZuGQxJkMCO5qfY0DnO8xibiioUNCVh15CaG/zv7GrGNHmLpZ1PIM0ZXM0diUJ+89Wn5GKWo8SdEWVI6Vk4aTpFBfuxt7JnrgwE4NCBsHx1aDVQ8Obyu1nNEl02vrxFtVelod+Cc6+4NsSjq8m0jMSr8aNyQ6WmAwn+eerHzAUqRukCjP149OiqFH2rogmKX4J9iY75nQ9waCQQTjpncyCHtwF9A7l9lMe+kU07g0JWxFFuYxsOpK/Ik7gLZzIy9nBsv9bUH2GKmo1StAVVUpWWhZrp32BABq19CVdV8DIsJGQlQQpB6FJnwr7XshyqQ9oNZpy89BLadIHTMVwchODQgdhr3cg6xZ39CZHjmyZQdzu2OozVlFrUYKuqDKklMz9YBImQzotczT8FplEc4/mRHpGmr1zqDB+DmYPXVMPUhYBtBoq99CDOoPOHmJX4ax3ZkCjAfxmv4vujk4gYfHXH1OYl199BitqJUrQFVXGmqlzyEzah1eBNwEjuhGTc4yRTUea88qPrwZHH/BtUWF/k0miqweFucC8GtZY2fINGzto1K30i3Bk2EjyDfkkjGpJk1QNxQVn+fPDz1TxrnqOEnRFlZBw4AB7ls3ERhtEp8Jk/mySjr3OnkGhg8Bkgrg1Zu+8Eg+8PsXQL6+2WC6Nb4a0Y5CZQEuvloS5h/G7aTPtWwTgIkNJjt3GtnmLqsdgRa1ECbrC6uSdz2T+px8hNM60jT+F2xMP88+pZQxoNABnvTMk74O8tErj51CS5VJPBF1XWR76BS68XsdXI4RgVNgoDqUfIv3e/kQd3YHWJphNf0wh6djRqjdYUStRgq6wKiajkb8nfkRxQS5BsgkNfHSsbJxPviGf0c1HmxvFrjL/G9qr0rHMHnr9eItqNQJjZTdFAbzCwKVB6es3OHQwDjoHZhdsxHdgbyLOFoJw4O9JE8jPzqoGqxW1jfrxaVFUGxtm/cbZuIM4ut5M8/0L8HrheeYc+4NW3q2I8IwwN4pdBX4twcmn0rHqlYeurSQP/QJCmMMucevAWIyT3okhjYew7MQybMbcS1DyDnxcelCQfZ6FX3yCyaTy0+sbStAVVuPYji3sXPQXWn0rWp3YjUv71hxoasOJrBOMblbineelw6mtEHalXQ1VDL1cwvpD4XlI2ALA6GajKTYVsyB3Mx733kvkjlnYOt1M4sG9bPlzdhVbrahtKEFXWIX0M6dZ+t0XCK0fjQPa4p6wHZ+XX2L2kTl42HnQv1F/c8NjK0CaIGzgFcesT3nouoqqLV5OaG/z6tojywBo4t6EDn4dmHtkLu5jHsFRW0ALnQGtPpKtf80ibveOKrZcUZtQgq64booLClj4+UcYi8HF9zYarf4a5wEDyAz1Zl3iOoY3HY5eqzc3ProMnHwhoG3lgwIGo/LQy2DrBCE9zK9jCaObjeZM7hk25+7Hc8wYfNZNISCkLxqdD/98+xmZZ5Or0HJFbUIJuuK6kFKy/KdvSUtMQGs/iHb2J9DlZeLz/HPMPToXgDvC7jA3Nhab4+dN+4EFNzuN9SoP3YIslwuEDYD045B6DIDewb3xsfdh9uHZeNx3LzY+3kTGzsXWdSiGIiMLP/+Q4sKCKrReUVuwZIOLX4UQKUKIAxWcF0KIb4QQsUKIaCFEO+ubqait7Fm6kMOb1mFj35VmrSOwX/ADbneMwhTox59H/6RnYE/8nfzNjU9uNsd/LYifQz3McrHEQwdzHB3giLl8ro3GhlHNRrHpzCZOFCXh/ewzaHavp12EI1q7AZw7eYKVP3+vFh3VAyz5tEwFKvsEDgSaljzGAv93/WYpbgROHdzP2ulTsHNphqN3N5ocnInG3h7vp59mcdxiMgozuC/ivv86HF0GWltzoSkLqFdZLpVVW7wct2DzCtuLwi6jwkah1+j5/eDvuN5+O7ZhYXjO/5QGYa2xde7KwQ1r2LNscRVZr6gtXFHQpZTrgfRKmgwDfpNmtgJuQgh/axmoqJ1kp6Wy+KtJ2Dl6ITW30DVKULR2OV6PP4bWw4PpB6cT7hFOlG+UuYOUZo8ypAfoHS26Rv3KctEgpbncgUWEDYCEreasIcDT3pMhjYew8PhCMouz8H39NQyJp2jndAidXWccPZqzbvovJB4q94e2oo5gjd+zDYBTFz1PLDlWBiHEWCHETiHEznPnzlnh0oqawFBUxKIvPqYovwCTZiDhXYKxnfU5Ng0a4H7ffWw6s4m483HcF3Hff/uBph6FjHhoZlm4BepZlkvJvQKLvfRmA0EaIXZl6aF7w++l0FjI3KNzcezaFaeePSn637d0HhCAwdQHOydPFn05kez01KqYgqIWYA1BL+8TV+67Ukr5k5QySkoZ5e3tbYVLK6obKSUrp0wmKfYITt6DcfYKoKXdYQoPH8bn5ZfQ2NryW8xv+Nj7MKDRReJdEu+1NH4O9c1DN8/T4jh6QDtzcbMj/21D18S9CTcF3MSsw7MoMhbh8+ormPLz8d31B4HN/ZC6W80ZSZ99iKGoqCqmoahhrCHoiUDQRc8DgTNWGFdRC9mzbDExa1cS0LwfBXnB9B4VQub3X2Hfpg3OAwZwNOMoW5K2cFf4Xdhobf7reGSpeXWoa6DF16pvMXTA8kwXjQbC+pk9dENh6eH7I+4nNT+VpfFLsW3cGPc77yTzjzl0626Ljd4Lj6DbSD5+jJW/qJukdRFrCPpC4P6SbJfOwHkpZZIVxlXUMhIORLP2t58JaNaWtORIWvYOxHb57xhT0/B9602EEPx+8HfsdfaMChv1X8esM+bVoeHDrup65jz0+pPlAlfhoYP59SzMgri1pYe6BHShiVsTph+cjpQSr2eeRuPkRO63n9DtjqacTwugUZuBxKxbxZ5lqjJjXcOStMVZwBagmRAiUQjxiBDicSHE4yVNlgBxQCzwM/BklVmrqDEyzyaz6KuJuPkGkJ/XC48AJ9q3FqRPn47byBHYt2xJcm4yi+IWMazxMFxtXf/rfLBki7TI267qmkaTpJ5sKVoq6BbH0MFc3MzOFWLmlR4SQnB/xP0cyTjCpjOb0Lm74/P8c+Rt20ZA5j4at/Xm7KlwgiKjWPvbL5yM3mvdiShqFEuyXO6SUvpLKW2klIFSyilSyh+klD+UnJdSyqeklI2llC2llDur3mxFdVKYl8f8T8YjTSY8gu6gsEBD34fCSfvkYzQODni/8AIA02KmgYSHWjx06QAx88ybHHs1varrGmX989AtznIB0Omh+RA4/M8lYZfBoYPxc/Tj5+ifAXC74w5sw8NJ+eQTegxviIOLLYVFvfEICGLRVx+Tfua0VeeiqDnqx6dFcc2YTEaWfPsp6WcSadV3DKePQedhjbE9vJXczVvwfvZZdB4epOWn8efRP7k19FYCnAL+G+B8IpzaBpFXF26B+hpDv8q4duRt5rDLhS39AButDQ9GPsjulN3sOrsLodXi987bGJKTyfn9V/o8GE5WqhH/5veg0WiZ/8l4CnJyrDgbRU2hBF1RKRtmTiNu9w46D3+IQ1u0BDZ3p1UXT1ImTsI2LAz30XcCMOPQDAqNhTzS8pFLB7gQbom4/aqvbTCa6lGWi/mjeFUxdICQnmDndknYBWB40+F42HmUeukO7drhMnQI6b/+io/tedrcEkTsrgKihj3F+ZSzLPpqIiajKrd7o6MEXVEh0auWsXPR37S6ZRAnDwWg02u55cEIUr//nuIzZ/B7dxxCpyOrKItZh2fRt2FfQlxDLh0kZp45u8WryVVfX3nolnTUQ/hgOLwEiv+r12Kvs+e+CPOagJi0GAB8X3kFYWdH8nvv02loKN7BzkSvMdLtrjEk7N/Lql//T2W+3OAoQVeUy4l9u1n5y2RC2rRHa9eT9DO53PJQBNozx0n/7Tfc7rgDh/btAZh9eDY5xTmMaTXm0kEyEyBxB0RevXcOJXno9aQ4139ZLhamLV5M5O1QlA3HV11yeHSz0Tjrnfkl+hcAdN7e+Lz0EnnbtpHzzyL6j4lEmiQnD/oSNXQE0SuXsXPxvPKuoLhBUIKuKMO5hBMs+vJjvIIaEt7jIQ5tOku7/g0Jbu5G0rh30bq74/PSiwDkFOUw/eB0ujfoTnOP5pcOVBpuue2a7FAeuoWE9AR79zJhFye9E3c3v5uVCSs5kn4EALc7RmHfti0pkybhqCuk173NORufhc7uJsK6dGf9779ydNum656PomZQgq64hOz0VOZNfB+9nT03P/wKG+aexC/UlY5DQ8iYMYOCAwfwfeN1tK7mtMTpB6eTWZjJU22fKjvYgb/ArxV4Nr5qO6SU9a7aIphz76++sw2EDzEv3irKveTUfRH34WzjzHd7vwNAaDT4vf8expwcUiZOommUL5E9GrB3RSIR3e/DP6w5S7/9nDNHD133nBTVT/34tCgsoiA3h78/epfCvBwGv/A26+ckodVp6PdoJMakJFK++hrH7t1xGTQIgIyCDKYdnEbfhn2J9Iy8dLCzB+HMHmh91zXZcsFRrTceuvYaFhZdTKvRUJQDBxdectjV1pWHWjzE2lNr2ZuyFwC7sDA8H3mE8wsWkLNhI91GNcE72JnVv8fS+8GXcfL0ZN6k8aQlnip7HUWtRgm6AjAX3Frw6QTSz5xm6EtvcWBDEZnJufR7NBInNz1Jb5pXgvq/925pwa0p+6eQb8jnqTbleOd7fgeNDbS689rsKYkl17csl2sKuQA07AoeoebX/TLuCb8HDzsPvtnzTelNT68nn0AfGkrSO+8g8nMZMLYFQgPrZp5k2CvvodFq+eujcaqQ1w2GEnRFSa75ZyQeOsDAp18k46wHsTtT6HxbY4Kae5AxcxZ527fj8/pr2DQwF9JMzk1m1uFZDA4dTGO3y0IqhiKIng3NB4Gj5zXZdMFTrTce+rUs/b8YIaDtvXByI6Qdv+SUg40DY1uNZUfyDrYmbQVAY2tLwMSPMaSkcHbiJFy87On3cCRpZ3LZsyKT4a+/R2Ge+RebylG/cVCCXs+RJhPLf/yWY9s30/uBMTh6tGDz38cJbeNN237BFJ08Scrnn+PYoztuI0eW9vsx+kdMmHii9RNlBz26FPLSoO19Zc9ZyAVPtf546FdZnKs8Wt8FQgN7Z5Q5NSpsFP6O/nyz+z8v3b5VKzzHjOH833+TvWYNwZGedBoSwtFtZ0mK0zP0pbdIP3Oavye9R1FB/rXbpag2lKDXY6SUrPntZ2LWrqTLyLsIbd+Xf386gLufA30eDAeTiTNvvoXQ6fD/4IPSUMuxjGPMOzaPkU1HEuhcTvXEPb+DcwA0vvmabTMalYd+1bgEQJO+sHcmGA2XnNJr9TzZ5kkOpB1gafx/JXe9nnoS27AwksaNw5CRQfsBjWjc1pvNf8UiCWTwc6+SfOwoCz6doEru3gAoQa/HbJ47gz1LF9H+1mG0HTiKfyZHIzSCW59shd5OR+oPP5C/axd+b7+Fja8vYP4SmLRjEg42DjzZppw6bFlnzCVd29wNGu0121bqodeT6lzXVJyrPNreC9lJl5QCuMCQ0CGEe4Tz+a7PySvOA0Cj1xMw8WOMmedJevsdENDnwQg8A51YPiUGj6BW9H/iORIO7GPx15MwGgxlxlXUHurHp0VRhq1/zWbrX7NpeXM/ut39MCumxJCVms/Ax1vi4mVP3s6dpH4/GZehQ3Ad9l8dltWnVrMtaRtPtXkKdzv3sgPvnQnSBG3vuS776l8MvWTp/7WkLV5M2ABw8II9v5U5pdVoeb3j66TkpfDrgV9Lj9tFRODz0ovkrFpFxsyZ2NhqGfREK3R6LUsmRxParjt9Hn6C4zu3seTbz5So12KUoNdDtv41m01//E5Ej5vp8+iTrJtxhFOHMuh1TzMCmrhhzMzk9CuvYhMYiN+4d0v7FRoL+XTHpzR2bcwdze4oO7DJCLt/g0bdzRkX10H9y3Kxkoeu00Pr0eac9Kyy2xK0823HwJCBTI2Zyumc/6osejzwAI49e5Ay6RMKDh/G2cOOQU+0JPd8Ef9Mjiay9wB63f8oR7duVKJei1GCXs+4WMz7P/EcO/9J4PCWZDrc2ojwrgFIKTnz9tsYUlNp8PnnaJ3+29D5t5jfOJ1zmtc6voaNxqbs4IcXQ+ZJ6Dj2uu2sdx769eahX0yHR8xfrtt/Kvf0i+1fRCM0fL7z89JjQggCPv4Yrasrp198CVNeHn4hrvR7OJKUE1ks/yWGtgOG0vO+R5So12KUoNcTpJRsnP3bJWJ+cGMyO5ecIPwmfzoMNhfVSp8yhZyVq/B54QXsW7Yo7X865zQ/7/+Zm4NupktAl/IvsvlbcA+B5rdet731LctFI6yQ5XIBj1Bzwa6dU6CwbMqhn6MfD7d4mBUnV7Dx9MbS4zoPDwI+/YSiEydIevttpJSEtvWmx+gwTkSnsm72UdrfelupqC/6cqK6UVrLsEjQhRADhBBHhBCxQojXyznfSwhxXgixt+QxzvqmKq4VaTKx+n8/sm3eH7S8uR/9n3iOuD1prJ91hIYtPOl1dzOEEORs3ETKF1/iPGAAHg89+F9/KXlv83sIBK93LPO/30zCNnMhri5PXdfN0AuY6pmgX/glYrJWtcOuz0LB+XJTGMG8CUmIawjjt4wnt/i/cgGOnTvj/cLzZC1ZSvqv/wOgRc9A2g9oyMENZ9i2MI6owbdz80OPcXznVuZNel+lNNYiLNmCTgt8DwwEIoC7hBAR5TTdIKVsU/IYb2U7FdeIyWhk2f99xd5/F9N+8O30HfsMJ/ens2JKDH6NXek/pgUarYaiU6c4/dJL2DZpQsCHE0pTFAHmx85na9JWXmz/Iv5O/uVfaPM35gJRbe62it2GehZyua5aLuUR1BGCOsGW78ukMALYam0Z33U8ybnJfLnry0vOeT76KM79+5Py+efkbDIX6uo0LJSI7gHsWnqSnUtP0HbAEAY8+QKnYvbz54fvqMVHtQRLPPSOQKyUMk5KWQTMBq5++xlFtVNUkM/8T8ZzcP1qut5xDz3vfZhTh9JZ9vMBvIKcGPxUa2xstZhyc0l8+hkAAr/7Fo3jf3HzlLwUPt3xKe192zOq2ajyL5R23LwNWtQjoHcsv81VYiz10OtHVNCqMfQLdHnafE/jcPmbQbfxacM94fcw58gcdib/t3OkEIKAjz7EtnFjzrz4EkUJCQgh6HVXM5p18mPbgjj2rkwgsmcfhrz4Oilxscx+91WyzqVYz3bFNWHJp6UBcHGVnsSSY5fTRQixTwixVAgRWc55hBBjhRA7hRA7z507dw3mKiwlNzODOe+9zonoPfQd8zRdRtxF4qEMlv7fftz9HBnybBv09jpkcTGJz79AYWwsDT77DH1wcOkYUkombJ1AkamI97u+j0ZU8HbZOtlc8c8KN0MvUG89dGsKevNbzfc0Nn8LFYRynmn7DA2cGvDu5nfJN/wXOtE4OhL43bcAnBozFkNGBkIjuPn+5jRu582mP2PZt/oUTTt2ZcSb48lJT2PmOy+TciLOevYrrhpLBL28T9Tl747dQEMpZWvgW2B+eQNJKX+SUkZJKaO8vb2vylCF5aSeOsnMt18m/Uwit736Dq1uGUB8dCqLJ+/D1ceBYc+1wc7RBiklSe+/T+6GDfi9Ow6n7t0uGWfu0bmsObWGZ9o+Q0OXhuVfLPMU7J5uLsLl7Gu1ORjrWdqi7lq3oKsMjRa6Pg2nd0HsqnKbONg48H7X90nITmDS9kmXnNM3bEjg/02mOCmJxCeexFRQgEaroe/DkYS28WbjH8fYtewEQZGtGD3+EzQaLbPffY24PTusNwfFVWGJoCcCQRc9DwTOXNxASpklpcwp+XsJYCOE8LKalQqLid2xlZlvv4yxuIg7351IaNsOHNt5lmU/7MergRO3vdgWe2c9AKmTJ3P+z7/wfOJx3O+4NK/8SPoRJm2fxE0NbuK+iEpqsqz5yPxvz9esOg9DPVv6XyUeOpjr6bg1hJXvmlMZy6GTfyceafEIfx37iyVxSy4559CuHQGffkr+vn2ceeUVpNFoLqk8JpKmHXzZOj+OrQuO4xkYzN0TPsPdL4B5k8azfcGfaju7GsASQd8BNBVChAgh9MBo4JKiy0IIP1FyF00I0bFk3DRrG6uoGCklW/+azYLPJuAREMg9H3+JX+OmHFh/mhVTYvANdWHY822xczTnj6f/PoPUb7/DddgwvJ999pKx8orzeHndy7jZuvFRt48qDrUk74d9s6DTY+AWVH6ba8RYT7NcrmkLukoHtoU+4+DsAYj+o8JmT7d9mrY+bXl/y/uczDp5yTmX/v3wfeN1slesJGncOKTJhFar4ZaHIgi/yZ9dS0+yfvZRHNw8GP3+JMI6d2PDzKks+fYziosKrTsfRaVcUdCllAbgaeBf4BDwh5QyRgjxuBDi8ZJmI4EDQoh9wDfAaKm+nquN/Jxs5n/6AZv++J3wbr248/2JOLl5smVeLOtmHiG4hSdDnjHHzAEyZs/m7IQJON3SB/8JH1yS0SKl5IOtH5CQncDEHhPxsPOo+MIr3wM7V+j+otXnVBpDr2d7ilrdQweIHA7+bWD1hEs2kr4YnUbHJz0+wUZrwyvrXqHQeKkQe9x/P15PPsH5v/4m+f3xSCnRaAS972lOm77BHFh3mqU/7Adhw+DnXqXb6Ps5vGkds95+mfQzp8u9psL6WJRCIKVcIqUMk1I2llJ+WHLsBynlDyV/fyeljJRStpZSdpZSbq5KoxX/kXTsCL+//hwn9u6m1/1jGPj0SwihY8WvMez+N4HIHg0Y9HhLbGzNueEZc+eS/N77OPXqReAXXyBsLl3x+dvB31gct5jHWz9OB78OFV84bq25CFf3l8zpilam3mW5XPDQrZW2eDEaDfQdD1mJsP3HCpv5Ofox4aYJHEo/xLhN48qETLyeeQbPMWPInDOHsx9MQEqJ0AhuGtGEHqPDOLk/lflf7CYvq4hOt9/B7a+/S3ZaKr+/8TyHN6+3/rwUZagfn5Y6iMlkZPuCP5n9rjl2PXr8JNrfOoycjELmfbabYztT6HJ7Y3reFYampGJh+u8zSB73Lo7du9Pgm68Rev0lY646uYrPd35Ov4b9eKzVYxVf3GiA5e+Aa5BVM1suRmW5WJnQnubSuhs+h9yKdyHqFdSLZ9s+y5L4JUzeN/mSc0IIvF98AY+HHiJj5kyS330PaTTH5Vv2CmTg4y1JP5PL3I93khx/ntC2Hbhv0td4BTfkn68/YflP36pFSFWMEvQbkPMpyfzx/htsmDmVxu07cu/Er/Fv0ozEIxn88dEOMs7mMfDxlrTr3xAhBFJKUr7+2hxm6d2bwG+/QXOZmB9IPcDrG16npVdLPuz2YcVxczAvIkqONnt9NnZVMsf6luUihECrEdbNcrmcfhOgOB/+eanSZo+2fJTbmtzGD/t+YNHxS3PYhRD4vPoKno89RuYff3D6+ecxFZrDMyGtvRn+anu0OsG8z3cTs+E0Ll4+3PnuRDoMHcH+1cuZ/uqznD6iNqCuKpSg30BIk4l9K5Yw7ZVnOHcyngFPvsCQF9/A1sGJnUtOsPDrvdg72TDq9ShC25jTQqXBQPK4d0n7vx9wGzWSwG++RmN3qQifzDrJM6ufwdPek29u/gY7XSUinXII1n4M4UMh8vYqm2t989DB/OVVZR46gE9zczbSwflw4O8KmwkhGNd5HB39OjJu8zg2n95c5rzPC8/j++abZK9YyalHHsWYlQWAd5Azo97oQIMwd9bOOMKqqQcxGqDHPQ9x57iPMZmMzHn3Ndb9/ivFheXH8xXXjhL0G4TUUyeZ/e5rrPxlMv5NmvLAp98T2bMPORmFLPhyD9sWxtG4nTcjX4vC3c+8WtOQkUHCo2PInDsXz8cfw2/8eIROd8m4J7NO8vCyhzGajEzuMxlP+0r2ADUWw7zHwdYZbv3CvI9lFVHfslzA/OVl9SyXy7npeQhoa/bScype2WmjteGLXl/Q2LUxz655toyoA3jcfx8Bn39G3r59nBh1B4WxsQDYOdow+OnWRA1qxJFtycz5cAdn47MIjGjB/Z98R4vet7Bz0d9Me+VpTkTvqaqZ1kuUoNdyCvPyWD/jf0x/7TnSk04z4MkXGPn2hzh7eXN4axJzJmznXEI2fR4Mp98jkaWZLAUHD3JixEjyd+/G/+OP8Xn++UuyWeA/MS82FTOl/xRC3a5Qw3zTV5C0F279HJyqdmHYf3no9ectWuUeOoBWB7f9AEU58M+LFa4gBXC1deXnfj/TyKVRhaLueuutNJz6P4y5uZy4406yV64EQKMRdBoaym0vtsNkNPH3p7vYvjgend6Ofo89yx3jPkKj0fLXh+/wzzefkpWqVo5bg/rzabnBMJmM7F+9nF+fH8uOhX8R3q0nD33xf0T27ENWagGLvtnLqqmHcPdz5M63O9C8s39pvDxj9mxO3H0P0mSi4YwZuN1+W5nxj6QfuUTMm7o3rdyguHWwdqI5zFKFoZYLlHro9SRtES546NWQ7evTHHq/BYcWwbaKs14A3O3cLxH1NQlryrRxaN+ekD/nom/ShMSnn+HsJ59iKimrG9DUjdFvd6Rxex92LI7nj492kBx3nqDIVtz/ybd0HnEXsdu38L8XHmfz3BkqDHOdiJpKF4+KipI7d+68csN6hpSS2B1b2DTnd9ISEwgIC6f3A2PwaxKGocjI3pWn2LX0BEIr6HJbY1r0aIC4kCGRmkrSW2+Ts24djl27EvDJJHReZRfsrk9czyvrXsFJ78QPt/xwZTFPPQa/9AFnf3hkuTn3vIqZuS2BN+ftZ+sbffBzrZobr7WNqAkr6Bfpx0e3t6z6i5lM8Md9cGQJ3DUbwvpX2jyjIIMnVz5JTFoML0W9xP0R95f5xWcqLOTsxx+TOXsOts2aEfDpJ9iFhZWeP7E/lXUzj5CTWUhktwA6DQ3F3llP1rkU1s34H0e3bMDR3YNOt99By5v7o7MpZxMVBUKIXVLKqHLPKUGvHUiTibg9O9jy5yzOxsXi7t+Am+68l7DO5voqsbtS2Px3LDnphYS28abbHU1x9jALnZSSrH+WcPajjzDl5uLz0ku433sP4rJwhZSS3w/9zmc7P6O5R3O+vflbfBx8KjcsN80s5oXZMGYVuDeqiumXYfrWk7wz/wA73roFb2fbarlmTdPpo5X0bubDxBGtqueCRbnwv4HmapkP/wt+LSptnm/I562Nb7Hi5ApGNB3BW53ewkZbVnSz16wh6e13MGVn4/X003g++EBpimxRgYFtC+PYv/Y0NnoNUYNCaNU7EK2NhtOHD7Jh1jROH47BxduHTrffQUSPPkrYL0MJei3GaDBweNM6diz8i7TEBFy8fegy4i4ietyM0Gg4uT+N7YvjOZeQjWegE91HNaVBs/8W8hQeP07y+A/I27YNu5YtCfj4I2ybNClzncyCTN7f8j4rE1ZyS/AtfNjtQxxsHCo3rjAHZoyE07vhwcXmGtvVxNRN8by36CB73umLu6P+yh3qADdNXE2Xxp58Nqp19V00Kwl+vhmEBh5eCm7BlTY3SRPf7fmOn/f/TKRnJB93/5gQ15Ay7QxpaSS/P57s5cvRh4biN24cjp07lZ5PT8pl81+xnDyQhrOHHe0HNqR5F380WsHJ6D1smjOd5OPHcHT3oN3AobTuOxBbB+uUZr7RUYJeC8lOTyV65b/sX7WM3MwMvIIb0WHoCJp16Y7QaInfd47dy06ScjIbFy87ogY1ollnfzQXwivnzpH6409kzJmDxt4enxdfwG3UKIS27G5Bm89s5p2N75BemM6zbZ/lgcgHKs8zB/PikxmjIGkfjPgFWgyvipehQn7ZEMeEfw4R/V4/XOzqh4fW45M1tG/ozpd3tqneCyftg2lDwMYB7v0bfMvbv+ZSVp5cyXtb3qPIWMTLUS8zKmxUmRAMQM66dSRP+JDiU6dw7tsX7+eevcThSDiYxraF8aScyMLZ0452/RvSrLMfOhsNJ/fvZceCP0k4sA8bO3siuvemTb9BeAU3subsbziUoNcSDMXFxO/eQcz61cTt3o6UkpA27WnbfzCN2rSnqMDI4c1JRK85RVZqAS5edrQf2Ihmnf3Qlqz2NKSnkz51GunTpyOLinAbMQLv555F51k23fBc3jm+2v0VC48vJNQ1lIndJxLuGX5lQzMTYPrtcD4RRk2FZgOt/EpcmR/XHefjpYc5OL4/DnrdlTvUAW7+bC2RDVz59q621X/xswfh9+FQnAd3/wHBna/cJfcsb296m61JW+no15HXOr5GmHtYmXamggLSfv2V9Cm/YsrPx3XIELyefAJ9Q3NJZiklCTHpbF9sFnZbRx2R3RvQsmcDnNztOBsXy55lizi8eT3G4mICmkUQ2fNmmnXpXi+9diXoNYjRYCDx4AGObtvI0a2bKMjJxtHNnfDuvWnddxCuPr6cOZbJoU1JHN+dgqHYhH9jV1r3CSKktVfpsv3CuDjSp07j/IIFyKIiXG69Fe9nni79UFxMgaGAmYdn8uO+Hyk2FXNfxH083vpx7HX2Vzb4+Bpzrrkh3+IPdlXw/ZpYPv33CEcmDMBWd/17lN4I9P1iHU19nZh8T/uaMeDiL/IBE6H9g1dca2CSJuYemcs3e74hpziHO5vdyROtn8Ddrmx9H0NGBmk//0LGjBnIoiKc+tyM54MPYt++fWmGVlLsefatOkXcvnMIIDjSk/Cu/jRq5UVRfg4H1qxg/5oVZJxJRGejJzSqE2GdbiK0bRQ2dvXj5rkS9GqmICeHE9G7ObF3F8d3bacgJxsbWztC23cksmcfglu05typXGJ3pXB8dwo56YXo7bQ07ehHxE3++DR0AcCUn0/28uVkzptP3tatCL0e12HD8Hjg/nLj5NlF2cw5MofpB6eTXpBOr8BevNLhFYJdKo+LAlCUZ66euP1H8AqDUdMs+uldVXyz6hhfrDjK8Y8G1ZvFRQO+Wk+whwM/3V/uZ7V6yE2FPx+G+HXQtB8M/Rac/a7YLbMgk+/2fsfco3Ox1doyoukIHoh8AD/Hsn0N586RPnMmmbNmY8zMxLZZM9yG347LkCHoPMzVPbNS8zm46QyHtySTm1mIrYOOkDbeNGnvQ4Nmbpw7EUvMutUc3bqR/Kzz6PS2NGzVltB2UYS0icLZs+5ux6AEvYopLijg9NFDnIqJ5tTB/SQfO4qUJuwcnQhpG0XTzjfh36QlyXF5nIxJIyEmjbzzRWi0guAID5pE+RLa1hsbvRZTXh45GzaSvWolOatWY8rNxSYoCLfht+N2552lb/iLOZR2iHmx81h8fDHZxdl0DejKoy0frbxa4gVMJvNS8NUTIP04dH7SXD/bxgJvvgr5YsVRvll1jPiPB5Ubm62LDP52A77Odkx50IL/b1WJyQQ7foYV75pr9fR8zeytW/CeiMuMY8qBKfwT9w9CCPoG9+X2prfTyb9Tmfs2pvx8zi9YSOaff1Jw4ADodDjddBPOfW/B6eab0Xl4YDJJTh1M59iOs8TvO0dRgRG9nZagcA+CW3gS2NyV82fjOLp1I8d3bic7zbxAySuoIUGRrQiKaElgRAvsnV2q4pWqEZSgWxGjoZi0xFOknIgjOfYoSceOcC4hHmkyITQa/Bo3JbhFG3xDWyLx5Wx8NqePZZJ2Ogck2DroCAr3oGFLT0JaeaG301J4+DC5W7aSu3Uredu3IwsL0bq64nRLH9xuuw37qKgyNctjM2NZl7iOf0/8y+H0w+g1evoE9+GBFg8Q6Vnulq6XTaTYvLHzukmQchC8msGgT81V+WoBn/57mB/XxRH70aCaNqXaGPb9JtzsbZj2cPVlE1VK6jHzatL49eY1CN1ehDZ3g63TFbuezjnN9IPTWXR8EVlFWQQ4BtA/pD+9g3rTyqsVWs2lYbSCo0c5P38B2cuWUXzmDGg02LdujWOXLjh26Yx969aYhI6EQ+mc2HeOkzHp5Gaai4K5eNkREOaOf2MX9HZZpCceJOHAXk4fOYihpHCYu38D/Js2w79JM3xCQvEODrlhQzRK0K+B4sICMs8mk5l0hrTTp0hLTCAtMYH006cwGgwA6O3t8Q0Nw80vBDvnhiD8yUwxcC4hm4KcYgB0Nhr8GrsS0NSNBk1d8bDJoij2GAUxMeTv20fB/gOYcnLM4zVujGPXrjj36YNDVPvSuitSSpJyk9h1dhe7zu5ia9JWTueYNw1o6dWSIY2HMChkEK62V1jwYzJB8j7zzjX750LuOfBsAr3eMK/+1NSeWPXHSw8xddMJjkyo/huyNcWI/9uMvY2W3x/tdOXG1Un8BvNWgwmbwcYRwodA6zuhUXfz5uCVUGgsZE3CGubHzmdb0jYM0oC7rTud/TvT3rc97Xzb0ditcan3LqWk8NAhsleuJGfjJrPnbjIh9HrswsOxb9MauxYt0DcNI9fOh8TYbM4cy+RMbCaFuebPpY2tFq8gJ9z97dDpUinIOUl2ygnOxh8l73ym2TAhcPdvgFdgMJ6BQXg0CMLdvwFufv7YOV75C6smuW5BF0IMAL4GtMAvUsqJl50XJecHAXnAg1LK3ZWNWZOCXlxUSF5mJnnnM8lJTyM7PY2cjDSyzqWQlZpC1rkUcjPSL+nj4OKJg5svto5+aGx8MZk8yctyID/bUNpGq9Pg7muPh4fAw7EQN5mO4/mTGBNOUHTiJIXx8cj8knrQWi22zcKwb90ahzZtcOjcBa2PF6n5qSRkJZCQnUBcZhxHMo5wJP0IGYUZADjrnWnv054eQT3oGdiz8oVBhTlw7rC5/sqJjeYPZl4qaPUQNgBaj4am/c31PWoZExYfZNb2BGLGD6hpU6qNO37cgkbA7LFdatqUskgJp7bB3pkQMx8Kz5vFvWFXCOkOAe3ANxIcKt7hKrsom02nN7E2cS07knaQkm8uDuagcyDMPYxmHs1o4taEYOdggl2C8XP0Q+Tkkbd9O3m795gdoJgYZEFJeQAbG/QNg9E3bIRNw4YUeIZwXutFeoEDaRmS9LMFFBf8t4+q3l6Lk1sxWl0a0pBCYV4y+Vlnyc04e8lmHnZOzrj6+OLi5YOLtzdO7p44eZgfjm7uOLq5Y2NnX2OhwOsSdCGEFjgK9MW8YfQO4C4p5cGL2gwCnsEs6J2Ar6WUlboZ1yPoUkqKCwsoys+nKD+Porw8CvPyyM/JIT8nl4LsHApycijIyTb/m5dDQU4WhbnZFObmYCgqW2RfCC06vQsanQtC44yUrpikG0LjitB6YN5OFQQSe5tiHDQFOMgcHIvSsM89i33GCfRJsYjc7EsH1miQfl4YGvhQ2MCT7CBPMgKdSfbVky5zySjMIC0/jbN5ZzmbdxaD6b8vCL1GT1P3pjTzaEa4e3PaerWiqVMDNIZCc3GlwmwozIK8dMhLM3vc509B5inIPAkZJ/6zwznAHE4J6WEW80o+eLWB9xbG8PfuRKLfq3xJel3i7p+3Umw0MffxrjVtSuUUF0DsCnN9n/j1kHrkv3NOfuARat5j1jUQnHzBwdP8sHMBWxfQOyF1diQWprM7bT8H0w5xOP0wRzKOkFucWzqURmjwsvfC18EXL3svPOw8cNc645dmwuN0Fs6nMrBPTEN3OgXNmRQoNlxqp60tBr/G5HmFku/oS56tF7kaF/KkPXnFekzSLMhSGpCmTKQxE43IRIjzILMxGrIwFJ1HmorLvARanR5bB2dsHZ2xc7rwrxP2Ts7YOTmW/O2EnbMjtg6O2Do4oLd3QG9vj42dHZrr+DV8vYLeBXhPStm/5Pkb5hdBfnxRmx+BtVLKWSXPjwC9pJRJFY17rYL+60svkJEYC1gQKhK2CGFX8q89aOwRwh4hHEHjgNA4oMEerUmHjRH0xnx0xbnYGPKxKc7GpjgHfVEOtkXn0Reex7YoE31RFhpposAGcu0gxx6y7eG8gyDTETKdBBlOkOoCqS6CNBcwllNgSkiJiwlcjeBulHgZJd5GEz4GE0HFRoIMBvyLDdhhRIcBHQY0Fsw5TXiQovEiWfhyUhtEvKYRcdpGJAvfKi13a21SsgvRCNgzrl9Nm1Jt3DdlG9vj0wn2uMIK3lqGuymDxqZ4GhlPEmI6iZ/pLD6mc3jLVLRcuRxwETqM6ChGS4pOR4JOxykbLck6Lee0gnM6QYZWcF4jOK8FYznvY2GSeOSAZxZ4ZUk8s8E1V+KaC265Eud8cM4Hx3ywKwKBoNjGiUJbNwptXSnUu1Js40SR3pliGyeKbRwp1jlQrHPAoNVQrDFgogBMeUiZizTlIWU+yHykKR9kAVIWgCzEEm2ys/PlqWlTruXlrlTQLfmt3QA4ddHzRMxe+JXaNAAuEXQhxFhgLEBwsAWpdOXg5O1OflIA4qL/NJj/BwkhEZgQSIQ0IjRGoBhzFOg8kiKQxUiKkKZCpCzCpC3GpBMU66FAaxZfoxaMOoFRBwadwKgTGGw0GGzAoHfGoNeYd5gBNAg0EnQIdFJghyBIChojsJECmxyBrdRii8DOpMFearCXWuylBiHMlkvAhBYpBBINJhsNaXoN59BgEDYYhRaj0FEsbCkWeoqFnkKNAwUljxytKzlaV3K1LhhF2Zimc8njRqKprxNtg6y/V2lt5p5ODXG2q33hryvjxHmC2Afsu+iokEYcjdk4mc7jZMzEzpiHnSkPO5mHjakQG1mEjSxCJ4vRSoP5gREbaaIJJpoaTQiDRBRe+FyDxEQhJvKFkTxhpECYKBSSQmGiSJgodpXmh5AUIMkVkgQkJgFGwIjEhERXVPIoPo+uOANdMWiNEp1BojVItEbQGEv+NYHeKBEmLRqTLWCLRuoR0gbQg8YGs5Q6IU1uSKFFokEikNIs7+bPOCVXl9i6VM3/Z0tGLc+tu/wryJI2SCl/An4Cs4duwbXLcMfr466lm0JR6xnQwo8BLa6c861QVIQl9dATgaCLngcCZ66hjUKhUCiqEEsEfQfQVAgRIsx3BkcDCy9rsxC4X5jpDJyvLH6uUCgUCutzxZCLlNIghHga+Bdz2uKvUsoYIcTjJed/AJZgznCJxRywfqjqTFYoFApFeVgUmZdSLsEs2hcf++GivyXwlHVNUygUCsXVoPYUVSgUijqCEnSFQqGoIyhBVygUijqCEnSFQqGoI9RYtUUhxDng5DV29wJSrWjOjYCac/1Azbl+cD1zbiil9C7vRI0J+vUghNhZUS2Duoqac/1Azbl+UFVzViEXhUKhqCMoQVcoFIo6wo0q6D/VtAE1gJpz/UDNuX5QJXO+IWPoCoVCoSjLjeqhKxQKheIylKArFApFHaFWC7oQYoAQ4ogQIlYI8Xo554UQ4puS89FCiHY1Yac1sWDO95TMNVoIsVkI0bom7LQmV5rzRe06CCGMQoiR1WlfVWDJnIUQvYQQe4UQMUKIddVto7Wx4L3tKoRYJITYVzLnG7pqqxDiVyFEihDiQAXnra9fUspa+cBcqvc4EAroMe9uFXFZm0HAUsw7JnUGttW03dUw566Ae8nfA+vDnC9qtxpz1c+RNW13Nfx/dgMOAsElz31q2u5qmPObwKSSv72BdEBf07Zfx5x7AO2AAxWct7p+1WYPvSMQK6WMk1IWAbOBYZe1GQb8Js1sBdyEEP7VbagVueKcpZSbpZQZJU+3Yt4d6kbGkv/PAM8AfwEp1WlcFWHJnO8G/pZSJgBIKW/0eVsyZwk4CyEE4IRZ0A3Va6b1kFKuxzyHirC6ftVmQa9o4+mrbXMjcbXzeQTzN/yNzBXnLIRoANwO/EDdwJL/z2GAuxBirRBilxDi/mqzrmqwZM7fAeGYt6/cDzwnpTRVj3k1gtX1qzZvMW61zalvICyejxCiN2ZB71alFlU9lsz5K+A1KaXR7Lzd8FgyZx3QHugD2ANbhBBbpZRHq9q4KsKSOfcH9gI3A42BFUKIDVLKrCq2raawun7VZkGvj5tTWzQfIUQr4BdgoJQyrZpsqyosmXMUMLtEzL2AQUIIg5RyfrVYaH0sfW+nSilzgVwhxHqgNXCjCrolc34ImCjNAeZYIUQ80BzYXj0mVjtW16/aHHKpj5tTX3HOQohg4G/gvhvYW7uYK85ZShkipWwkpWwE/Ak8eQOLOVj23l4AdBdC6IQQDkAn4FA122lNLJlzAuZfJAghfIFmQFy1Wlm9WF2/aq2HLuvh5tQWznkc4AlMLvFYDfIGrlRn4ZzrFJbMWUp5SAixDIgGTMAvUspy099uBCz8//wBMFUIsR9zOOI1KeUNW1ZXCDEL6AV4CSESgXcBG6g6/VJL/xUKhaKOUJtDLgqFQqG4CpSgKxQKRR1BCbpCoVDUEZSgKxQKRR1BCbpCoVDUEZSgKxQKRR1BCbpCoVDUEf4fPbzDw4PtfQsAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sol = prob.Solve(\"theta\", 0.6)\n",
    "prob.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "1427f737-1ea6-4126-b671-b8a7e3159a3d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cdt/dx^2 is: 0.6\n",
      "using explicit method\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sol = prob.Solve(\"explicit\")\n",
    "prob.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "73cbd7b0-a194-474b-aeab-a9b55b9f55c6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cdt/dx^2 is: 0.6\n",
      "using implicit method\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sol = prob.Solve(\"implicit\")\n",
    "prob.plot()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
